1. Efficient Allocation of a Non-renewable Mineral Resource Over Time Wednesday, March 2

2. Number 1 P = 8 – 0.4 q P 0 = 8 – 0.4(8.004) = 4.80 P 1 = 8 – 0.4(7.305) = 5.08 Etc. P = MEC + MUC MUC 0 = 4.80 – 2.00 = 2.80 MUC 1 = 5.08 – 2.00 = 3.08 Etc. 2.80(1.1) = 3.08 3.08(1.1) = 3.39 Etc. MUC increases at the rate of discount (10%)

3. #1 - Graph P, MEC and MUC over time

4. Impacts on optimal extraction rates when market conditions change  Number 2 When a renewable substitute is added  Number 3 When marginal extraction costs are an increasing function of quantity extracted  Numbers 4 and 5 Options for efficiency and sustainability

5. Number 2 P = 8 – 0.4 q P 0 = 8 – 0.4(8.798) = 4.48 P 1 = 8 – 0.4(8.177) = 4.73 Etc. P = MEC + MUC MUC 0 = 4.48 – 2.00 = 2.48 MUC 1 = 4.73 – 2.00 = 2.73 Etc. 2.48(1.1) = 2.73 2.73(1.1) = 3.00 Etc. MUC increases at the rate of discount (10%)

6. Number 2 (continued)  MUC does not increase at the rate of discount between periods 4 and 5. Why?  What is the maximum price you would expect for the resource in period 5? Why? $6.00 = 8 – 0.4q 0.4q = 2 q = 5 If q = 5, q of depletable is 2.863 units q of renewable is 2.137 units

7. #2 - Graph P, MEC and MUC over time

8. Impacts on optimal extraction rates when market conditions change  When a renewable substitute is added: Opportunity cost of use is lower The resource is used more quickly

9. P = 8 – 0.4 q P 0 = 8 – 0.4(7.132) = 5.15 P 1 = 8 – 0.4(6.523) = 5.39 Etc. MEC = 2 + 0.1q MEC 0 = 2 + 0.1(7.132) = 2.71 MEC 1 = 2 + 0.1(13.66) = 3.37 MEC 2 = 2 + 0.1(19.68) = 3.97 Etc. (In this case, q is the cumulative amount extracted.) Number 3

10. Number 3 (continued) P = MEC + MUC MUC 0 = 5.15 – 2.71 = 2.44 MUC 1 = 5.39 – 3.37 = 2.03 MUC 2 = 5.59 – 3.97 = 1.63 MUC is not increasing at the rate of discount. Why?

11. #3 - Graph P, MEC and MUC over time

12. What happens to MUC over time if MEC is increasing? TIME $ MEC MEC + MUC = P = MUC

13. Impacts on optimal extraction rates when market conditions change  When marginal extraction costs are an increasing function of quantity extracted: Opportunity cost is lower The resource is used more slowly since cost is increasing

14. Increases in demand  Increases in population, income, etc.  Expect higher prices for any level of extraction  This means opportunity cost of current extraction is higher  So MUC is higher for every time period than if demand were constant.  What does this mean for the rate of extraction?

15. Sustainability efforts – building a capital stock (Number 4)  PV of total net benefits from mineral resource is $152.17.  For a perpetuity:  So  Payment = $15.22  At t=0, NB=$35.22 Keep $15.22, put 20.00 into fund  At t=1, PV NB=$33.17 Keep $15.22, put 17.95 into fund  In PV terms Keep $13.84, put $16.32 into fund  Etc.

16. Sustainability efforts – building a capital stock (Number 5)  PV of net benefits is $152.17  In period 0, $35.22 is used  So, period 0 needs to deposit into capital fund enough to insure there is $35.22 at the start of year 8 (first year after mineral is depleted)  x(1.1) 8 = 35.22  2.144x = 35.22  X=16.43 – to be paid into fund at time 0  16.43(1.1) 8 = 35.22 – will be in fund at time 8

17.  PV of net benefits is $152.17  In period 1, $30.15 is used (in PV terms)  So, period 1 needs to deposit into capital fund enough to insure there is $30.15 at the start of year 8 (first year after mineral is depleted)  x(1.1) 7 = 30.15  1.949x = 30.15  X=15.47 – to be paid into fund at time 0  15.47(1.1) 7 = 30.15 – will be in fund at time 8

18. Alaska Permanent Fund  www.apfc.org www.apfc.org  What is the purpose of the Permanent Fund? According to language in the state law which established the Permanent Fund (AS 37.13), the Permanent Fund was created with three purposes: (1) to provide a means of conserving a portion of the state's revenue from mineral resources to benefit all generations of Alaskans (2) to maintain safety of principal while maximizing total return (3) to be a savings device managed to allow maximum use of disposable income for purposes designated by law

19. Policy Question  When Price exceeds MEC, does that mean that the mine owner is earning excess profits and they should be taxed away?  What happens to extraction rate if rents are taxed away?

20. $ $ $ $ Use money now Save and use more money later OR Your Savings Account

21. Why would taxing away rents result in faster rate of resource extraction? $ mineral Mine and use income now Save, mine later, and use income later OR Q mineral

22. Why would taxing away rents result in faster rate of resource extraction?  If mine owner does not get to keep rent, the incentive is to extract the resource quickly and invest the returns in some alternative income-earning venture e.g. Extract the mineral, sell it, and invest the money at some positive rate of growth

23. P t = MEC t + MUC t  Can predict changes in price by predicting changes in MEC or MUC  E.G. start of war in Middle East Oil prices rise Price gouging? Or increase in MUC? Once more certainty in availability is established, MUC goes back down